In the case of a thin metallic slab, empirical models have been quite thoroughly explored. Upon the introduction of a boundary to an infinite metallic slab, a negative (begrenzung) peak is introduced at the same energy as the bulk peak, and a trailing surface peak appears. [1]} The surface peak becomes more pronounced with decreasing thickness, as does the negative begrenzung peak, decreasing the net bulk-plasmon amplitude. A sharp transition can be observed, between \(34\,\) nm and \(10\,\) nm Ag film thickness, in which surface modes become dominant. This transition can also be observed for Au and Cu films, between \(34\,\) nm and \(20\,\) nm. This is consistent with observations in the well-validated and widely-used empirical data by Johnson and Christy. [2]}
